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Abelian group angle answer associative law base vectors beginning point bisect Calculate can/cannot Cartesian equation Cartesian form Check your results commutative law coordinates definition dependent diagonals Diagram 12b direction cosines displacement vectors distributive law does/does dot product draw a diagram Examples expression Flow Diagram 13b Flow Diagram 6a given i+j+k is/is line/plane linear linearly independent mid point move multiply negative normal notation numbers numerical value orientation origin pairs of vectors parallel parallelepiped parallelogram plane/line position vector Pretest Programme 17 prove prpouct radius ratio Reorganize represents the translation results Flow Diagram scalar product scalar triple product scalar variables Similarly Simplify small letters sphere of centre straight line Strategy subtract successive translations Summary tangent plane three dimensions three vectors triangle trisect unit vector variable scalar vector equation vector product vector representing vectors are equal volume Write written xi+yj xi+yj+zk zero